Generalized interval-valued Pythagorean fuzzy aggregation operators and their application to group decision-making

For the multiple-attribute group decision-making problems where the attribute values are the interval-valued Pythagorean fuzzy numbers, the group decision-making method based on some generalized interval-valued Pythagorean fuzzy aggregation operators is developed. First, generalized interval-valued Pythagorean fuzzy weighted geometric (GIVPFWG) aggregation operator, generalized interval-valued Pythagorean fuzzy ordered weighted geometric (GIVPFOWG) aggregation operator, and generalized interval-valued Pythagorean fuzzy hybrid geometric (GIVPFHG) aggregation operator were developed. Some basic properties of the proposed operators, such as idempotency, commutativity, monotonicity and boundedness, were discussed, and some special cases in these operators were analyzed. The methods and operators proposed in this paper are providing more general, more accurate and precise results as compared to the existing methods because these methods and operators are the generalization of their existing methods. Furthermore, the method for multiple attribute group decision-making problems based on these proposed operators was developed, and the operational processes were also illustrated in detail. Finally, an illustrative example is given to show the decision-making steps in detail of these proposed methods and operators to show the validity, practicality and effectiveness.